1.) Field of the Invention
This invention relates to tomography and, more particularly, to a method and concomitant system wherein an image of an object is directly reconstructed from measurements of scattered radiation using a limited set of data for reconstruction.
2.) Description of the Background Art
The inventive subject matter addresses the physical principles and the associated mathematical formulations underlying the direct reconstruction method for optical imaging in the multiple scattering regime. Methodologies for the direct solution to the image reconstruction problem result. Moreover, the methodologies are generally applicable to imaging with any scalar wave in the diffusive multiple scattering regime and are not limited to optical imaging. However, for the sake of elucidating the significant ramifications of the present inventive subject matter, it is most instructive to select one area of application of the methodologies so as to insure a measure of definiteness and concreteness to the description. Accordingly, since many biological systems meet the physical requirements for the application of the principles of the present invention, especially photon diffusion imaging principles, the fundamental aspects of the present inventive subject matter are conveyed using medical imaging as an illustrative application of the methodologies.
There have been three major commericial developments in medical imaging that have aided in the diagnosis and treatment of numerous medical conditions, particularly as applied to the human anatomy; these developments are: (1) the Computer-Assisted Tomography (CAT) scan; (2) the Magnetic Resonance Imaging (MRI); and (3) the Positron Emission Tomography (PET) scan.
With a CAT scanner, X-rays are transmitted through, for example, a human brain, and a computer uses X-rays detected external to the human head to create and display a series of images-basically cross-sections of the human brain. What is being imaged is the X-ray absorption function for unscattered, hard X-rays within the brain. CAT scans can detect, for instance, strokes, tumors, and cancers. With an MRI device, a computer processes data from radio signals impinging on the brain to assemble life-like, three-dimensional images. As with a CAT scan, such malformations as tumors, blood clots, and atrophied regions can be detected. With a PET scanner, the positions of an injected radioactive substance are detected and imaged as the brain uses the substance. What is being imaged is the gamma ray source position. Each of these medical imaging techniques has proved invaluable to the detection and diagnosing of many abnormal medical conditions. However, in many respects, none of the techniques is completely satisfactory for the reasons indicated in the following discussion.
In establishing optimal design parameters for a medical imaging technique, the following four specifications are most important. The specifications are briefly presented in overview fashion before a more detailed discussion is provided; moreover, the shortcomings of each of the conventional techniques are also outlined. First, it would be preferable to use a non-ionizing source of radiation. Second, it would be advantageous to achieve spatial resolution on the order of a millimeter to facilitate diagnosis. Third, it would be desirable to obtain metabolic information. And, fourth, it would be beneficial to produce imaging information in essentially real-time (on the order of one millisecond) so that moving picture-like images could be viewed. None of the three conventional imaging techniques is capable of achieving all four specifications at once. For instance, a CAT scanner is capable of high resolution, but it uses ionizing radiation, it is not capable of metabolic imaging, and its spatial resolution is borderline acceptable. Also, while MRI does use non-ionizing radiation and has acceptable resolution, MRI does not provide metabolic information and is not particularly fast. Finally, a PET scanner does provide metabolic information, but PET uses ionizing radiation, is slow, and spatial resolution is also borderline acceptable. Moreover, the PET technique is invasive due to the injected substance.
The four specifications are now considered in more detail. With respect to ionizing radiation, a good deal of controversy as to its effects on the human body presently exists in the medical community. To ensure that the radiation levels are within what are now believed to be acceptable limits, PET scans cannot be performed at close time intervals (oftentimes, it is necessary to wait at least 6 months between scans), and the dosage must be regulated. Moreover, PET is still a research tool because a cyclotron is needed to make the positron-emitting isotopes. Regarding spatial resolution, it is somewhat self-evident that diagnosis will be difficult without the necessary granularity to differentiate different structures as well as undesired conditions such as blood clots or tumors. With regard to metabolic information, it would be desirable, for example, to make a spatial map of oxygen concentration in the human head, or a spatial map of glucose concentration in the brain. The ability to generate such maps can teach medical personnel about disease as well as normal functions. Unfortunately, CAT and MRI report density measurements—electrons in an X-ray scanner or protons in MRI—and there is not a great deal of contrast to ascertain metabolic information, that is, it is virtually impossible to distinguish one chemical (such as glucose) from another. PET scanners have the ability to obtain metabolic information, which suggests the reason for the recent popularity of this technique. Finally, imaging is accomplished only after a substantial processing time, so real-time imaging is virtually impossible with the conventional techniques.
Because of the aforementioned difficulties and limitations, there had been a major effort in the last ten years to develop techniques for generating images of the distribution of absorption and scattering coefficients of living tissue that satisfy the foregoing four desiderata. Accordingly, techniques using low intensity photons would be safe. The techniques should be fast in that optical events occur within the range of 100 nanoseconds—with this speed, numerous measurements could be completed and averaged to reduce measurement noise while still achieving the one millisecond speed for real-time imaging. In addition, source and detector equipment for the techniques may be arranged to produce necessary measurement data for a reconstruction procedure utilizing appropriately-selected spatial parameters to thereby yield the desired one millimeter spatial resolution. Finally, metabolic imaging with the techniques should be realizable if imaging as localized spectroscopy is envisioned in the sense that each point in the image is assigned an absorption spectrum. Such an assignment may be used, for example, to make a map of oxygenation by measuring the absorption spectra for hemoglobin at two different wavelengths, namely, a first wavelength at which hemoglobin is saturated, and a second wavelength at which hemoglobin is de-saturated. The difference of the measurements can yield a hemoglobin saturation map which can, in turn, give rise to tissue oxygenation information.
As a result of this recent effort, a number of techniques have been developed and patented which satisfy the four desiderata. Representative of the technique whereby both absorption and scattering coefficients are directly reconstructed is the methodology, and concomitant system, reported in U.S. Pat. No. 5,747,810 (“Simultaneous Absorption and Diffusion Tomography System and Method Using Direct Reconstruction of Scattered Radiation”) having Schotland as the inventor (one of the inventors of the present inventive subject matter). In accordance with the broad aspect of the invention in '810, the object under study is irradiated by a continuous wave source at a given frequency and the transmitted intensity due predominantly to diffusively scattered radiation is measured at selected locations proximate to the object wherein the transmitted intensity is related to both the absorption and diffusion coefficients by an integral operator. The absorption and diffusion images of the object are directly reconstructed by executing a prescribed mathematical algorithm, determined with reference to the integral operator, on the transmitted intensity measurements. In addition, radiation at different wavelengths effects imaging as localized spectroscopy.
Another technique, covered in U.S. Pat. No. 5,905,261 (“Imaging System and Method Using Direct Reconstruction of Scattered Radiation” also having Schotland as one of the inventors) discloses and claims explicit inversion formulas obtained from the observation that it is possible to construct the singular value decomposition of the forward scattering operator within the diffusion approximation. In accordance with the broad aspect of '261 for imaging an object having variable absorption and diffusion coefficients, the object under study is irradiated and the transmission coefficient due predominantly to diffusively scattered radiation is measured at appropriate locations proximate to the object. The transmission intensity is related to the absorption and diffusion coefficients by an integral operator. An image representative of the object is directly reconstructed by executing a prescribed mathematical algorithm, determined with reference to the integral operator, on the transmission coefficient. The algorithm further relates the absorption and diffusion coefficients to the transmission coefficient by a different integral operator.
The art is devoid of techniques for dealing with: (1) effects of sampling, that is, placement of the sources and receivers in order to obtain sampled data, in the reconstruction process, as well as limiting the amount of data being processed; and (2) paraxial reconstruction wherein a single source is utilized to illuminate the object, with the scattered light being detected by an on-axis detector plus a small number of off-axis detectors, and then scanning the surface of the object with the source-detectors array while varying the frequency range of the source.
Moreover, whereas the prior art dealt with using data in a posterior manner to solve the fundamental integral operator relation devised by the prior art, the prior art is devoid of teachings and suggestion on the use of both sampled and limited data which are taken into account beforehand to solve the fundamental integral operator relation.